Scalar Hairy Black Holes with Inverted Mexican Hat Potential

TL;DR

This paper numerically constructs and analyzes asymptotically flat hairy black holes supported by an inverted Mexican hat scalar potential, revealing their properties and instability under linear perturbations.

Contribution

It introduces a new class of hairy black hole solutions with an inverted Mexican hat potential and studies their physical properties and stability.

Findings

Hairy black holes emerge from Schwarzschild solutions with scalar hair outside the horizon.

These black holes have specific properties like horizon area, temperature, and photon sphere.

They are linearly unstable under perturbations.

Abstract

We numerically construct the asymptotically flat solutions of hairy black holes supported by a symmetric inverted Mexican hat potential with a local minimum and two degenerate global maxima of a real scalar field that contains a quartic self-interaction term. The solutions of hairy black holes emerge from the Schwarzschild black hole when the non-trivial scalar field exists outside the event horizon. Therefore, we perform a comprehensive study on the properties of the hairy black holes such as the area of horizon, the Hawking temperature, the innermost stable circular orbit, the photon sphere, etc. We also numerically study their linear stability in the mode analysis, hence finding that they are unstable against the linear perturbation.